JP2018011022A - Oscillation device, calculation device, and measuring method - Google Patents

Abstract

PROBLEM TO BE SOLVED: To provide an oscillation device capable of adjusting a loss, and a calculation device and a measuring method.SOLUTION: An oscillation device includes a resonator, an electromagnetic wave application unit, a filter and a conductive unit. The resonator includes a Josephson junction. The electromagnetic wave application unit applies a first electromagnetic wave including a component of a first frequency, and a second electromagnetic wave including the component of the first frequency and a component of a second frequency to the resonator. The conductive unit transmits the electromagnetic wave passed through the filter. The resonator oscillates at a third frequency by the first electromagnetic wave, and oscillates at the third frequency and a fourth frequency by the second electromagnetic wave. A passage rate of the filter at the fourth frequency is higher than that of the filter at the third frequency.SELECTED DRAWING: Figure 1

Description

  Embodiments described herein relate generally to an oscillation device, a calculation device, and a measurement method.

  Computers using an oscillation device that exhibits quantum mechanical branching have been proposed. In such an oscillation device, it is desirable to be able to adjust the loss.

H. Goto, Sci. Rep. 6, 21686 (2016) H. Goto, Phys. Rev. A 93, 050301 (R) (2016)

  Embodiments of the present invention provide an oscillation device, a calculation device, and a measurement method that can adjust loss.

  According to the embodiment of the present invention, an oscillation device including a resonator, an electromagnetic wave application unit, a filter, and a conductive unit is provided. The resonator includes a Josephson junction. The electromagnetic wave application unit applies a first electromagnetic wave including a first frequency component and a second electromagnetic wave including a first frequency component and a second frequency component to the resonator. The conductive portion transmits electromagnetic waves that have passed through the filter. The resonator oscillates at a third frequency by the first electromagnetic wave, and oscillates at the third frequency and the fourth frequency by the second electromagnetic wave. The pass rate of the filter at the fourth frequency is higher than the pass rate of the filter at the third frequency.

It is a schematic diagram which illustrates the oscillation apparatus which concerns on embodiment. It is a top view which illustrates a part of oscillation device concerning an embodiment. It is a graph which illustrates the frequency characteristic of the filter of the oscillation device concerning an embodiment. It is a graph which illustrates the calculation result of the Kerr coefficient and parametric excitation amplitude in the 1st example. It is a graph which illustrates the calculation result of the resonance frequency of the higher order mode in the 1st example. It is a graph which illustrates the calculation result of the coupling coefficient of the fundamental mode in 1st Example, and a primary mode. It is a graph which illustrates the calculation result of the Kerr coefficient and parametric excitation amplitude in the 2nd example. It is a graph which illustrates the calculation result of the resonance frequency of the higher order mode in the 2nd example. It is a graph which illustrates the calculation result of the coupling coefficient of a fundamental mode and a primary mode in the 2nd example. It is a schematic diagram which illustrates the calculation apparatus which concerns on embodiment.

Each embodiment will be described below with reference to the drawings.
The drawings are schematic or conceptual, and the relationship between the thickness and width of each part, the size ratio between the parts, and the like are not necessarily the same as actual ones. Further, even when the same part is represented, the dimensions and ratios may be represented differently depending on the drawings.
Note that, in the present specification and each drawing, the same elements as those described above with reference to the previous drawings are denoted by the same reference numerals, and detailed description thereof is omitted as appropriate.

FIG. 1 is a schematic view illustrating an oscillation device according to the embodiment.
FIG. 1 schematically shows a part of the oscillation device 100 according to the embodiment in a circuit diagram.
As illustrated in FIG. 1, the oscillation device 100 according to the embodiment includes an oscillator 10, a filter 20, and a conductive unit 30. The oscillator 10 includes an electromagnetic wave application unit 11 and a resonator 12.

  The resonator 12 is a superconducting nonlinear resonator having a Josephson junction. The resonator 12 includes a superconducting part 121 and a superconducting part 122 joined to each other, and has a dc SQUID (superconducting quantum interferometer) structure. That is, the resonator 12 includes a loop (ring) 12 a provided by the superconducting portions 121 and 122. Superconducting portion 121 and superconducting portion 122 are joined to each other by Josephson junctions J1 and J2. Specifically, an insulator is provided between one end of the superconducting part 121 and one end of the superconducting part 122, and insulation is provided between the other end of the superconducting part 121 and the other end of the superconducting part 122. A body is provided. Thereby, the loop 12a is provided.

  The center of the resonator 12 is, for example, a waveguide 12b having a length L. That is, the superconductive portion 121 includes a waveguide 12b extending from the end of the loop 12a toward the outside of the loop 12a. In this example, a capacitor C0 (capacitance Cj) is provided between the superconducting portion 121 and the ground potential (ground). Superconducting portion 122 is connected to the ground potential.

  In the dc SQUID structure, the Josephson energy due to the Josephson junction can be controlled by the magnetic flux in the dc SQUID (Y. Makhlin et al., Rev. Mod. Phys. 73, 357 (2001)). The resonator 12 can oscillate in accordance with a change in magnetic flux in the loop 12a. There are a plurality of modes in the oscillation of the resonator 12. For example, the plurality of modes include a first mode and a second mode, and the resonator 12 oscillates at a third frequency f3 that is close to the first resonance frequency in the first mode, and reaches the second resonance frequency in the second mode. Oscillates at a near fourth frequency f4.

  The electromagnetic wave application unit 11 applies an electromagnetic wave to the resonator 12. An external current (external current for dc SQUID excitation) for exciting the dc SQUID mode flows through the electromagnetic wave application unit 11. That is, when a high-frequency current flows through the electromagnetic wave application unit 11, a varying magnetic field is generated. Thereby, the electromagnetic wave application part 11 can control the magnetic flux in dc SQUID (in the loop 12a).

  For example, the electromagnetic wave application unit 11 applies an electromagnetic wave including a frequency component of the first frequency f1 (first electromagnetic wave) to the resonator 12 and modulates the magnetic flux in the resonator 12 (in the dc SQUID). As a result, the first mode is excited, and the resonator 12 oscillates at the third frequency f3 close to the first resonance frequency.

  The third frequency is equal to the half value f1 / 2 of the first frequency f1. In the present specification, “the third frequency is equal to the half value (half) of the first frequency” includes a case where the third frequency and the half value of the first frequency are different within a range of variation in measurement.

  Alternatively, the electromagnetic wave application unit 11 applies an electromagnetic wave (second electromagnetic wave) including the frequency component of the first frequency f1 and the frequency component of the second frequency f2 to the resonator 12, and modulates the magnetic flux in the resonator 12. . As a result, the first mode and the second mode are excited, and the resonator 12 oscillates at the third frequency f3 close to the first resonance frequency and the fourth frequency f4 close to the second resonance frequency.

  The fourth frequency is equal to the sum f2 + f3 of the second frequency f2 and the third frequency f3. In the present specification, “the fourth frequency is equal to the sum of the second frequency and the third frequency” means that the fourth frequency and the sum of the second frequency and the third frequency are within the range of variation in measurement. , Including the case where they are different.

  The conductive portion 30 transmits the electromagnetic wave generated by the oscillation of the resonator 12 and having passed through the filter 20. For example, the conductive part 30 is a readout line and is electrically connected to a measuring instrument or the like. Thereby, the electromagnetic wave propagated from the resonator 12 through the filter 20 can be measured.

  The filter 20 is provided between the resonator 12 and the conductive portion 30 on the circuit diagram representing the oscillation device 100. As shown in FIG. 1, the filter 20 is capacitively coupled to the resonator 12 and the conductive unit 30. The filter 20 is capacitively coupled to the resonator 12 at the first position 201 of the filter 20, and capacitively coupled to the conductive portion 30 at the second position 202 different from the first position 201. In this example, the first position 201 and the second position 202 are the ends of the filter 20. The first position 201 and the second position 202 are not limited to the ends of the filter.

  For example, the end of the first position 201 of the filter 20 and the end 123 of the resonator 12 (waveguide 12b) are arranged to face each other. A capacitor C <b> 1 is provided between the end of the first position 201 and the end 123. Similarly, the end portion of the filter 20 at the second position 202 and the end portion 301 of the conductive portion 30 are arranged to face each other. A capacitor C <b> 2 is provided between the end of the second position 202 and the end 301.

  The filter 20 is a filter having frequency characteristics. The pass rate of the filter 20 at the fourth frequency f4 is higher than the pass rate of the filter 20 at the third frequency f3. For example, the filter 20 transmits the electromagnetic wave according to the second mode and does not pass the electromagnetic wave according to the first mode. For such a filter 20, for example, a λ / 2 waveguide resonator for an electromagnetic wave having the fourth frequency f4 can be used. That is, the length of the filter 20 (the length of the waveguide of the filter 20) is not less than 0.4 times and not more than 0.6 times the wavelength of the electromagnetic wave having the fourth frequency f4 in the waveguide, and is 0.5 times. Is desirable. In this example, the length of the waveguide of the filter 20 is the distance from the end of the first position 201 to the end of the second position 202 of the filter 20. However, the filter 20 may not be linear as illustrated in FIGS. 1 and 2, may be curved, and may have a plurality of linear portions. In this case, the length of the waveguide is the length of the path in the filter 20 from the end of the first position 201 to the end of the second position 202.

FIG. 2 is a plan view illustrating a part of the oscillation device according to the embodiment.
As illustrated in FIG. 2, the resonator 12 (the oscillator 10), the filter 20, and the conductive unit 30 (readout line) are wirings provided on the substrate 40, for example. These wirings contain, for example, aluminum (Al), niobium (Nb), etc., and are transferred to a superconductor by cooling. A conductive film 45 surrounding the wiring is provided on the substrate 40, and the conductive film 45 is connected to the ground potential. Thereby, the capacitor C0 shown in FIG. 1 is formed.

  No wiring is provided between the end portion of the first position 201 of the filter 20 and the end portion 123 of the resonator 12. Thereby, the capacitor C1 shown in FIG. 1 is formed, and the filter 20 and the resonator 12 are capacitively coupled. Similarly, no wiring is provided between the end portion of the second position 202 of the filter 20 and the end portion 301 of the conductive portion 30. Thereby, the capacitor C2 is formed, and the filter 20 and the conductive portion 30 are capacitively coupled.

  FIG. 3 is a graph illustrating the frequency characteristics of the filter of the oscillation device according to the embodiment. The horizontal axis in FIG. 3 represents the frequency f (hertz: Hz). The vertical axis in FIG. 3 represents the pass rate Ra of the filter 20. The pass rate Ra corresponds to the ratio of the amplitude of the electromagnetic wave output (applied) to the conductive portion 30 by the filter 20 with respect to the amplitude of the electromagnetic wave input (applied) by the resonator 12 to the filter 20.

  As shown in FIG. 3, the filter 20 is, for example, a bandpass filter, and has a passband B1. In the pass band B1, the pass rate Ra of the filter 20 has a peak (maximum value P1). The pass band B1 includes a fifth frequency f5 and a sixth frequency f6 higher than the fifth frequency f5. The pass rate of the filter 20 at the fifth frequency f5 is half the peak value (P1 / 2), and the pass rate of the filter 20 at the sixth frequency f6 is half the peak value (P1 / 2).

  The fourth frequency f4 is included in the passband B1. For example, the fourth frequency f4 falls within the range of the full width at half maximum of the frequency characteristic of the filter 20. In other words, the fourth frequency f4 is a frequency between the fifth frequency f5 and the sixth frequency f6. Thereby, the filter 20 allows the electromagnetic wave in the second mode to pass.

  On the other hand, the third frequency f3 is not included in the passband B1. For example, the third frequency f3 is lower than the fifth frequency f5. Alternatively, the third frequency f3 is higher than the sixth frequency f6. For this reason, the filter 20 does not pass the electromagnetic wave by the 1st mode. In the example shown in FIG. 3, the third frequency f3 is lower than the fourth frequency f4, but the embodiment is not limited to this example.

  As described above, the first mode is excited by the first electromagnetic wave including the component of the first frequency f1. The nonlinearity due to the Josephson junction may have a property that the resonance frequency decreases as the number of photons in the resonator increases, for example. For this reason, when used for quantum computation, it is desirable that the third frequency f3 equal to the half value f1 / 2 of the first frequency f1 is equal to or higher than the first resonance frequency. The first electromagnetic wave does not include a component of the second frequency f2, and the second mode is not substantially excited when the first electromagnetic wave is applied to the resonator 12.

On the other hand, the fourth frequency f4 (the sum of the second frequency f2 and the third frequency f3) is desirably equal to the second resonance frequency. In the embodiment, the difference (first difference) between the fourth frequency f4 and the second resonance frequency is made smaller than the width of the passband B1. For example, the first difference is set within the range of the full width at half maximum of the frequency characteristic of the filter 20. In other words, the first difference is smaller than the difference between the fifth frequency f5 and the sixth frequency f6.
Thereby, the first mode and the second mode are excited by the electromagnetic wave including the components of the first frequency f1 and the second frequency f2.

  Consider a case where the first mode is excited by the first electromagnetic wave including the component of the first frequency f1, and the resonator 12 oscillates at the third frequency f3. At this time, since the pass rate Ra of the filter 20 at the third frequency f3 is low, the electromagnetic wave of the third frequency f3 hardly propagates to the conductive portion 30 via the filter 20. Therefore, when the first electromagnetic wave is applied to the resonator 12, the energy loss of the resonator 12 through the filter 20 and the conductive portion 30 is small.

  On the other hand, the resonator 12 oscillates at the third and fourth frequencies f3 and f4 by the second electromagnetic wave including the components of the first and second frequencies f1 and f2. At this time, since the pass rate Ra of the filter at the fourth frequency f4 is high, the electromagnetic wave at the fourth frequency f4 propagates to the conductive portion 30 via the filter 20. Therefore, when the second electromagnetic wave is applied to the resonator 12, the energy loss of the resonator 12 is larger than when the first electromagnetic wave is applied to the resonator 12.

  As described above, in the oscillation device 100 according to the embodiment, the filter 20 is provided between the resonator 12 and the conductive portion 30. Thereby, the loss can be adjusted by controlling the magnetic flux in the dc SQUID.

  Such an oscillation device 100 can be used for a quantum computer, for example. For example, the combination optimization problem can be solved by utilizing the oscillation phenomenon of the network of the plurality of oscillation devices 100. In a quantum computer using a non-linear oscillator, it is desired to turn on / off reading so that the energy of the oscillator is not emitted as much as possible during the calculation and the energy can be extracted only when reading the calculation result.

  On the other hand, if the oscillator and readout line are capacitively coupled, it is difficult to completely turn off readout during the calculation. For this reason, it may be difficult to increase the on / off ratio of reading.

  On the other hand, when the oscillation device 100 is used in a quantum computer, the loss can be adjusted, so that the loss during calculation can be reduced. According to the embodiment, in the readout of the nonlinear oscillator mounted with the superconducting circuit having the Josephson junction, the on / off can be performed, and the loss of the oscillator can be extremely reduced at the time of the off.

Hereinafter, reading (measurement) of an oscillation state in the oscillation device will be described.
As already described, the resonator 12 has a plurality of modes. Hereinafter, the mode having the lowest resonance frequency is referred to as a fundamental mode, and the other modes are referred to as higher-order modes. Higher order modes are numbered as first order, second order, etc. in order from the lowest resonance frequency.

  Each of the first mode and the second mode described above can be arbitrarily selected from the basic mode and the higher-order mode. For example, the first mode can be the basic mode, and the second mode can be the primary mode.

  The resonator 12 has nonlinearity called Kerr effect due to Josephson junction. By changing the magnetic flux in the dc SQUID at a frequency (for example, corresponding to the first frequency f1) that is about twice the resonance frequency of the fundamental mode (for example, corresponding to the first resonance frequency), the Josephson energy is modulated. The fundamental mode is parametrically excited and oscillation occurs.

ここで、ａ_０は基本モードの消滅演算子、ａ_ｎはｎ次モードの消滅演算子を表す。係数Ｅ^（ｎ） _ｉｎｔは基本モードとｎ次モードとの相互作用の係数であり、ｄｃ ＳＱＵＩＤのジョセフソンエネルギーに比例する。 Due to the nonlinearity due to the Josephson junction, the interaction described by the following Hamiltonian exists between the fundamental mode and the higher-order mode (the fundamental mode is the oscillation angular frequency (half value of the parametric excitation angular frequency), Higher order modes are displayed in the rotating coordinate system of the resonance angular frequency).

Here, a ₀ is extinguished operator, a _n of the fundamental mode represents annihilation operators n-order mode. The coefficient E ⁽ⁿ⁾ _int is a coefficient of interaction between the fundamental mode and the n-th mode, and is proportional to the Josephson energy of the dc SQUID.

のために、上記の相互作用は無視され、高次モードは励起されない。しかし、ｄｃ ＳＱＵＩＤ内の磁束をこの角周波数差（ω_ｎ‐ω_ｐ／２）に等しい角周波数（例えば第２周波数ｆ２に対応する）で変調すると、ジョセフソンエネルギーがその角周波数で変調され、ハミルトニアンの中の上記の速い振動因子がキャンセルし、基本モードからｎ次モードへのエネルギー変換が起こる。その結果、角周波数ω_ｎ（例えば第４周波数ｆ４に対応する）の電磁波が発生する。 Normally, the difference (ω _n −ω _p / 2) between the oscillation frequency ω _p / 2 (close to the fundamental mode resonance angular frequency ω ₀ ) and the n-order mode resonance angular frequency ω _n is sufficiently large. For this reason, a fast vibration factor

For this reason, the above interaction is ignored and higher modes are not excited. However, when the magnetic flux in the dc SQUID is modulated with an angular frequency equal to this angular frequency difference (ω _n -ω _p / 2) (eg, corresponding to the second frequency f2), the Josephson energy is modulated at that angular frequency, The fast oscillation factor in the Hamiltonian cancels and energy conversion from the fundamental mode to the nth order mode occurs. As a result, an electromagnetic wave having an angular frequency ω _n (for example, corresponding to the fourth frequency f4) is generated.

Therefore, through the filter 20 through the electromagnetic wave of the angular frequency omega _n combine with the line reads the resonator 12 (conductive portion 30), to measure the electromagnetic wave condition of the angular frequency omega _n generated. The state of the basic mode can be read by this measurement. On the other hand, since the fundamental mode cannot pass through the filter 20, the energy of the fundamental mode does not come out unless there is modulation of the angular frequency (ω _n −ω _p / 2).

  As described above, by installing a filter that passes the n-order mode of the resonator 12 but does not pass the fundamental mode between the resonator 12 and the readout line, the loss of the fundamental mode is very small in the calculation. be able to. At the time of reading, frequency modulation corresponding to the difference between the oscillation frequency and the resonance frequency of the n-th mode is applied to the magnetic flux in the dc SQUID of the oscillator. As a result, the energy of the fundamental mode is converted into the n-order mode, and the generated n-order mode electromagnetic wave is taken out to the readout line through the filter and measured. Therefore, the basic mode state can be read. In this way, a large on / off ratio can be realized, and the loss of the fundamental mode at the time of off can be made very small.

  As described with reference to FIG. 3, the frequency setting is performed with the same accuracy as the bandwidth of the filter 20 (passband B <b> 1).

  The state readout method according to the embodiment can be performed simply by installing the filter 20 as a passive element between the resonator 12 and the readout line. In this state readout method, modulation necessary for readout can be performed by using the dc SQUID originally used for parametric excitation as it is. For this reason, there is an advantage that it is simpler than a method using a read line having a dc SQUID.

An embodiment using the circuit shown in FIG. 1 will be described below.
Here, the primary mode is used as a high-order mode used for reading.

とすると、この非線形発振器のハミルトニアンは、近似的に次のようになる。 The Josephson energy of the dc SQUID modulated by the external current for dc SQUID excitation

Then, the Hamiltonian of this nonlinear oscillator is approximately as follows.

ここで、

は、パラメトリック励起に対する基本モードの離調である。

here,

Is the detuning of the fundamental mode for parametric excitation.

ｐはパラメトリック励起振幅であり、次式で表される。

ｇ_ｒは、基本モードと１次モードとの結合係数であり、次式で表される。 K _n is the Kerr coefficient of each mode is expressed by the following equation.

p is a parametric excitation amplitude and is expressed by the following equation.

g _r is the coupling coefficient between the fundamental mode and the first-order mode is expressed by the following equation.

αｎは、定数であり、次式で表される。

ここで、φ_０は、磁束量子を２πで割ったものであり、次式で表される。

αn is a constant and is expressed by the following equation.

Here, φ ₀ is obtained by dividing the magnetic flux quantum by 2π and is represented by the following equation.

ｋ_ｎは、導波路中の各モードの波数であり、

および、

を満たす。ここで、Ｃ_ｗ、Ｌ_ｗは、導波路の単位長さ当たりのキャパシタンスとインダクタンスである。

k _n is the wave number of modes in the waveguide,

and,

Meet. Here, C _w and L _w are capacitance and inductance per unit length of the waveguide.

は、導波路の特性インダクタンスである。

Is the characteristic inductance of the waveguide.

は、ｄｃ ＳＱＵＩＤのジョセフソンインダクタンスである。

Is the Josephson inductance of the dc SQUID.

Hereinafter, description will be made by selecting specific values of parameters.
Typical values are C _w = 150 (femtofarad / millimeter: fF / mm), Zw = 50 (ohm: Ω), and ω ₀ / 2π = 5 (gigahertz: GHz).

とする。これで残りのパラメータはＣ_ＪとＬだけで決まる。以下、実施例１ではＣ_Ｊを比較的大きい値である１００ｆＦに、実施例２ではＣ_Ｊを比較的小さい値である１０ｆＦに設計した場合を説明する。

And This remaining parameters determined only by C _J and L. Hereinafter, the 100fF a relatively large value in _{C J} Example 1, illustrating the case of designing the in _{C J} Example 2 to a relatively small value 10 fF.

(First embodiment)
Here, the 100fF a relatively large value _{C J.} At this time, K ₀ and p are expressed as a function of L as shown in FIG.
FIG. 4 is a graph illustrating the calculation results of the Kerr coefficient and the parametric excitation amplitude in the first embodiment.
When L is a value close to 6 mm, K ₀ becomes small, and nonlinearity is small, which is not desirable. When L is close to zero, it is difficult to increase in comparison with the p K _0, undesirable as an oscillator. Therefore, in this case, L is preferably 1 mm or more and 4 mm or less.

FIG. 5 is a graph illustrating the calculation result of the resonance frequency of the higher-order mode in the first example.
FIG. 5 shows the resonance frequency of the higher-order mode when L is 1 mm, 2 mm, 3 mm, or 4 mm. It can be seen that the resonance frequency of the higher order mode is greatly deviated from the resonance frequency of 5 GHz of the fundamental mode. It can be seen that the difference between the resonance frequency of one higher order mode and the resonance frequency of another higher order mode is 10 GHz or more.

FIG. 6 is a graph illustrating the calculation result of the coupling coefficient between the fundamental mode and the first-order mode in the first embodiment. Figure 6 shows the L dependence of _{g r.} g _r is a maximum at L = 2.5mm around. The value of g _{r is} sufficiently large and _g r / _2π ≒ 140MHz. Therefore, it is possible to efficiently convert from the fundamental mode to the primary mode by modulation.

A filter that passes only the primary mode will be described. As an example, consider the case of L = 2.5 mm _{to g r} is maximized. At this time, the resonance frequency of the primary mode is 22.6 GHz. Therefore, a filter that passes 22.6 GHz is installed between the oscillator and the readout line. Such a filter can be implemented with a λ / 2 waveguide resonator having a fundamental mode resonance frequency of 22.6 GHz. For example, the capacitance per unit length of the waveguide and the characteristic impedance are set to 150 fF / mm and 50Ω, respectively, as described above. At this time, since the wavelength of 22.6 GHz is 5.90 mm, the length of the resonator may be half that of 2.95 mm. Since the resonance frequency of the fundamental mode of the oscillator is 5 GHz, electromagnetic waves in the fundamental mode cannot pass through this filter.

(Second embodiment)
Here, a 10fF a relatively small value _{C J.} At this time, K ₀ and p are expressed as a function of L as shown in FIG.

FIG. 7 is a graph illustrating the calculation results of the Kerr coefficient and the parametric excitation amplitude in the second embodiment.
When L is a value close to 6 mm, K ₀ becomes small, and nonlinearity is small, which is not desirable. L is the I 1mm or less, it is difficult to increase in comparison with the p K _0, undesirable as an oscillator. Therefore, in this case, L is preferably 2 mm to 4 mm.

FIG. 8 is a graph illustrating the calculation result of the resonance frequency of the higher-order mode in the second example.
FIG. 8 shows the resonance frequency of the higher-order mode when L is 2 mm, 3 mm, or 4 mm. It can be seen that the resonance frequency of the higher order mode is greatly deviated from the resonance frequency of 5 GHz of the fundamental mode. It can be seen that the difference between the resonance frequency of one higher order mode and the resonance frequency of another higher order mode is 10 GHz or more.

FIG. 9 is a graph illustrating the calculation result of the coupling coefficient between the fundamental mode and the first-order mode in the second embodiment. Figure 9 shows the L dependence of _{g r.} g _r is the maximum value in the vicinity of L = 2.3mm. The value of g _r is sufficiently large and _g r / _2π ≒ 145MHz. Therefore, it is possible to efficiently convert from the fundamental mode to the primary mode by modulation.

A filter that passes only the primary mode will be described. As an example, consider the case of L = 2.3 mm _{to g r} is maximized. At this time, the resonance frequency of the primary mode is 29.1 GHz. Therefore, a filter that passes 29.1 GHz is installed between the oscillator and the readout line. Such a filter can be implemented with a λ / 2 waveguide resonator having a fundamental mode resonance frequency of 29.1 GHz. The capacitance per unit length of the waveguide and the characteristic impedance are set to 150 fF / mm and 50Ω, respectively, as described above. At this time, since the wavelength of 29.1 GHz is 4.58 mm, the length of the resonator may be half that of 2.29 mm. Since the resonance frequency of the fundamental mode of the oscillator is 5 GHz, electromagnetic waves in the fundamental mode cannot pass through this filter.

(Third embodiment)
FIG. 10 is a schematic view illustrating a calculation device according to the embodiment.
As illustrated in FIG. 10, the calculation device 200 (quantum calculation device) includes a plurality of oscillation devices 100 and a coupled resonator 150. In this example, a first oscillation device 101 and a second oscillation device 102 are provided as the plurality of oscillation devices 100. The first oscillation device 101 and the second oscillation device are coupled via a coupled resonator 150.

The coupled resonator 150 includes a wiring part 52 (superconducting part), a resonator 50a, a resonator 50b, an electromagnetic wave application part 51a, and an electromagnetic wave application part 51b. The wiring part 52 is a waveguide.
The resonator 50a and the resonator 50b each have a dc SQUID structure. That is, each resonator is a loop-shaped superconducting circuit formed by two Josephson junctions. On the circuit, a resonator 50a is provided between one end of the wiring portion 52 and the ground potential, and a resonator 50b is provided between the other end of the wiring portion 52 and the ground potential.

  The electromagnetic wave application unit 51a can modulate the magnetic flux in the resonator 50a (dc SQUID) with current. Similarly, the electromagnetic wave application unit 51b can modulate the magnetic flux in the resonator 50b (dc SQUID) with current.

  The resonator 12 (superconducting portion 121) of the first oscillation device 101 is capacitively coupled to the wiring portion 52 of the coupled resonator 150 by the capacitor C3. Similarly, the resonator 12 (superconducting portion 121) of the second oscillation device 102 is capacitively coupled to the wiring portion 52 of the coupled resonator 150 by the capacitor C4.

  As described above, in the calculation device 200 according to the embodiment, each of the plurality of oscillation devices 100 is capacitively coupled to the coupled resonator terminated with the dc SQUID. Thereby, the oscillation devices 100 are coupled to each other via the coupled resonator, and a network of the oscillation devices 100 is formed.

  Although FIG. 10 illustrates the case where two oscillation devices 100 are coupled, in the embodiment, three or more oscillation devices 100 may be provided. In this case, the number of arms of the oscillation device 100 may be increased, and the coupled resonator 150 may be provided between each of the plurality of oscillation devices 100.

  As shown in FIG. 10, the computing device 200 is electrically connected to the measuring device 151 and the control device 152. The control device 152 individually controls a system parameter (referred to as a branch parameter) of each oscillation device 100. For example, the control device 152 controls the current of the electromagnetic wave application unit 11 of each oscillation device 100.

  The measuring device 151 is electrically connected to the conductive portion 30 (reading line) of each oscillation device 100. The measuring device 151 measures the output of each oscillation device 100 via the conductive unit 30. The calculation device 200 can obtain a calculation result from this measurement result. The measuring device 151 measures the parity of the phase of the electric field amplitude, for example.

The computing device 200 is used to solve a combination optimization problem, for example.
When the oscillation device 100 is used alone, it is possible to generate a superposition of distinguishable quantum states by branching one quantum state by quantum adiabatic change using a system parameter (branch parameter) as a control parameter. . It is assumed that the loss of the oscillation device 100 during the calculation is so small that the influence can be ignored. For example, the oscillation device 100 generates a quantum mechanical superposition of two oscillation states when the initial state is a vacuum state and the parametric excitation amplitude p (branch parameter of the oscillation device 100) is gradually increased from zero. .

  The computing device 200 using a plurality of such oscillation devices 100 finds an optimal solution using a quantum adiabatic change whose initial state is vacuum. In the calculation, the coupling between the oscillation devices 100 is set according to the problem to be solved. For example, the Hamiltonian of the network of the oscillation device 100 can be considered using the Ising model as an example. The setting of the coupling between the oscillation devices 100 corresponds to the setting of the coupling constant between Ising spins.

  After setting the connection, gradually change the branch parameter. At the beginning of the calculation, the bifurcation parameter is zero, and the initial vacuum state is the ground state of the entire system. If the bifurcation parameter is changed sufficiently slowly, the state of the whole system changes to the final Hamiltonian ground state by the quantum adiabatic theorem. Here, when the branching parameter is sufficiently large, the nonlinear term (parametric amplification and Kerr effect) is the main, the oscillation amplitude is the same in any oscillation device, and only the phase is different. And this phase is measured from each oscillation apparatus 100, and a calculation result is obtained from a measurement result.

  As described above, the combination optimization problem can be solved by utilizing the oscillation phenomenon (branch phenomenon) and the quantum effect by the network of the oscillation device 100.

  It is also possible to couple the two oscillation devices 100 directly via a capacitor. However, when the two oscillation devices 100 are directly coupled, the degree of freedom of arrangement of the oscillation devices 100 is low and it is difficult to change the coupling constant. Therefore, in the example of FIG. 10, the oscillation devices 100 are coupled together by the coupled resonator 150. Thereby, the freedom degree of arrangement | positioning improves. By adjusting the coupling strength between the oscillation device 100 and the coupled resonator 150 and the detuning of the coupled resonator 150, the coupling constant can be easily changed according to the problem to be solved.

Embodiments may include the following configurations, for example.
(Configuration 1)
A resonator including a Josephson junction;
An electromagnetic wave application unit configured to apply a first electromagnetic wave including a first frequency component and a second electromagnetic wave including the first frequency component and the second frequency component to the resonator;
Filters,
A conductive part for transmitting electromagnetic waves that have passed through the filter;
With
The resonator oscillates at a third frequency by the first electromagnetic wave, oscillates at the third frequency and the fourth frequency by the second electromagnetic wave,
An oscillation device in which a pass rate of the filter at the fourth frequency is higher than a pass rate of the filter at the third frequency.
(Configuration 2)
The third frequency is equal to half of the first frequency;
The oscillation device according to Configuration 1, wherein the fourth frequency is equal to a sum of the second frequency and the third frequency.
(Configuration 3)
The pass rate of the filter at a fifth frequency included in one pass band of the filter is half of the peak value of the pass rate of the filter,
The pass rate of the filter at a sixth frequency included in the passband and higher than the fifth frequency is half of the peak value,
The fourth frequency is between the fifth frequency and the sixth frequency;
The oscillation device according to Configuration 1 or 2, wherein the third frequency is lower than the fifth frequency or higher than the sixth frequency.
(Configuration 4)
Any one of configurations 1 to 3, wherein the filter is capacitively coupled to the resonator at a first position of the filter and capacitively coupled to the conductive portion at a second position of the filter different from the first position. Oscillator described in one.
(Configuration 5)
The oscillation device according to any one of configurations 1 to 4, wherein a resonance frequency of the resonator closest to the third frequency is equal to or lower than the third frequency.
(Configuration 6)
The oscillation device according to any one of configurations 1 to 5, wherein the electromagnetic wave application unit modulates a magnetic flux in a loop of the resonator.
(Configuration 7)
The filter includes a waveguide;
The length of the said waveguide is an oscillation apparatus as described in any one of the structures 1-6 which are 0.4 times or more and 0.6 times or less of the wavelength in the said waveguide of the electromagnetic wave of the said 4th frequency.
(Configuration 8)
The resonator has a plurality of resonance frequencies;
The oscillation device according to any one of configurations 1 to 7, wherein a resonance frequency of the resonator closest to the third frequency is the lowest among the plurality of resonance frequencies.
(Configuration 9)
A plurality of the oscillation devices according to any one of configurations 1 to 8 are provided,
The plurality of oscillation devices include a first oscillation device and a second oscillation device,
The first oscillating device and the second oscillating device are coupled to each other.
(Configuration 10)
Further comprising a coupled resonator including a wiring portion,
The calculation device according to Configuration 9, wherein the first oscillation device and the second oscillation device are coupled via the coupled resonator.
(Configuration 11)
The computing device according to Configuration 10, wherein the coupled resonator includes a Josephson junction provided between one end of the wiring portion and a ground potential.
(Configuration 12)
The calculation device according to Configuration 11, wherein the coupled resonator further includes an electromagnetic wave application unit that modulates a magnetic flux in a loop of the coupled resonator.
(Configuration 13)
The calculation device according to any one of Configurations 10 to 12, wherein the first oscillation device is capacitively coupled to the wiring portion of the coupling resonator.
(Configuration 14)
A method of measuring an oscillation state of a resonator having a loop having a Josephson junction and oscillating at a second frequency equal to a half value of the first frequency by modulating a magnetic flux in the loop at a first frequency,
In addition to modulating the first frequency, applying the third frequency modulation to the magnetic flux of the loop causes the resonator to oscillate at a fourth frequency equal to the sum of the second frequency and the third frequency. ,
Take out the electromagnetic wave of the fourth frequency to the readout line through a filter that passes the electromagnetic wave of the fourth frequency,
A measurement method for measuring the electromagnetic wave of the fourth frequency in the readout line.
(Configuration 15)
Applying a first electromagnetic wave including a component of a first frequency to a resonator having a Josephson junction;
Applying a second electromagnetic wave including the first frequency component and the second frequency component to the resonator;
Measuring electromagnetic waves propagated from the resonator through a filter;
A method for measuring the oscillation state of the resonator,
The resonator oscillates at a third frequency by the first electromagnetic wave, oscillates at the third frequency and a fourth resonance frequency by the second electromagnetic wave,
A measurement method in which a pass rate of the filter at the fourth frequency is higher than a pass rate of the filter at the third frequency.
(Configuration 16)
The third frequency is equal to half of the first frequency;
The measurement method according to Configuration 15, wherein the fourth frequency is equal to a sum of the second frequency and the third frequency.
(Configuration 17)
The pass rate of the filter at a fifth frequency included in one pass band of the filter is half of the peak value of the pass rate of the filter,
The pass rate of the filter at a sixth frequency included in the passband and higher than the fifth frequency is half of the peak value,
The fourth frequency is between the fifth frequency and the sixth frequency;
The measurement method according to Configuration 15 or 16, wherein the third frequency is lower than the fifth frequency or higher than the sixth frequency.
(Configuration 18)
Any one of configurations 15 to 17, wherein the filter is capacitively coupled to the resonator at a first position of the filter and capacitively coupled to a conductive portion at a second position of the filter different from the first position. The measuring method as described in.

  In the embodiment, the electrically connected state includes a case where the plurality of conductors are connected via other conductors in addition to a state where the plurality of conductors are in direct contact. The state of being electrically connected includes the case where a plurality of conductors are connected via elements having functions such as switching and amplification.

  According to the embodiment, it is possible to provide an oscillation device, a calculation device, and a measurement method that can adjust the loss.

The embodiments of the present invention have been described above with reference to specific examples. However, embodiments of the present invention are not limited to these specific examples. For example, regarding the specific configuration of each element such as a resonator, an electromagnetic wave application unit, a filter, and a conductive unit, those skilled in the art can implement the present invention in the same manner by appropriately selecting from a well-known range, and obtain the same effect. As long as it is possible, it is included in the scope of the present invention.
Moreover, what combined any two or more elements of each specific example in the technically possible range is also included in the scope of the present invention as long as the gist of the present invention is included.

  In addition, all oscillation devices, calculation devices, and measurement methods that can be implemented by those skilled in the art based on the oscillation device, calculation device, and measurement method described above as embodiments of the present invention are also included in the present invention. As long as the gist is included, it belongs to the scope of the present invention.

  In addition, in the category of the idea of the present invention, those skilled in the art can conceive of various changes and modifications, and it is understood that these changes and modifications also belong to the scope of the present invention. .

  Although several embodiments of the present invention have been described, these embodiments are presented by way of example and are not intended to limit the scope of the invention. These novel embodiments can be implemented in various other forms, and various omissions, replacements, and changes can be made without departing from the scope of the invention. These embodiments and modifications thereof are included in the scope and gist of the invention, and are included in the invention described in the claims and the equivalents thereof.

  DESCRIPTION OF SYMBOLS 10 ... Oscillator, 11 ... Electromagnetic wave application part, 12 ... Resonator, 12a ... Loop, 12b ... Waveguide, 20 ... Filter, 30 ... Conductive part, 40 ... Substrate, 45 ... Conductive film, 50a, 50b ... Resonator, 51a , 51b ... Electromagnetic wave application unit, 52 ... Wiring unit, 100-102 ... Oscillating device, 121, 122 ... Superconducting unit, 123 ... End, 150 ... Coupling resonator, 151 ... Measuring device, 152 ... Control device, 200 ... Computation device 201 ... first position 202 ... second position 301 ... end B1 ... passband C0-C4 ... capacitor Cj ... capacitance J1, J2 ... Josephson junction L ... length P1 ... Maximum value, Ra ... pass rate, f1 to f6 1st to 6th frequency

Claims (10)

A resonator including a Josephson junction;
An electromagnetic wave application unit configured to apply a first electromagnetic wave including a first frequency component and a second electromagnetic wave including the first frequency component and the second frequency component to the resonator;
Filters,
A conductive part for transmitting electromagnetic waves that have passed through the filter;
With
The resonator oscillates at a third frequency by the first electromagnetic wave, oscillates at the third frequency and the fourth frequency by the second electromagnetic wave,
An oscillation device in which a pass rate of the filter at the fourth frequency is higher than a pass rate of the filter at the third frequency. The third frequency is equal to half of the first frequency;
The oscillation device according to claim 1, wherein the fourth frequency is equal to a sum of the second frequency and the third frequency. The pass rate of the filter at a fifth frequency included in one pass band of the filter is half of the peak value of the pass rate of the filter,
The pass rate of the filter at a sixth frequency included in the passband and higher than the fifth frequency is half of the peak value,
The fourth frequency is between the fifth frequency and the sixth frequency;
3. The oscillation device according to claim 1, wherein the third frequency is lower than the fifth frequency or higher than the sixth frequency.   The oscillation device according to claim 1, wherein the electromagnetic wave application unit modulates a magnetic flux in a loop of the resonator. The filter includes a waveguide;
5. The oscillation device according to claim 1, wherein a length of the waveguide is not less than 0.4 times and not more than 0.6 times a wavelength of the electromagnetic wave having the fourth frequency in the waveguide. . A plurality of the oscillation devices according to any one of claims 1 to 5,
The plurality of oscillation devices include a first oscillation device and a second oscillation device,
The first oscillating device and the second oscillating device are coupled to each other. Further comprising a coupled resonator including a wiring portion,
The calculation device according to claim 6, wherein the first oscillation device and the second oscillation device are coupled via the coupled resonator. A method of measuring an oscillation state of a resonator having a loop having a Josephson junction and oscillating at a second frequency equal to a half value of the first frequency by modulating a magnetic flux in the loop at a first frequency,
In addition to modulating the first frequency, applying the third frequency modulation to the magnetic flux of the loop causes the resonator to oscillate at a fourth frequency equal to the sum of the second frequency and the third frequency. ,
Take out the electromagnetic wave of the fourth frequency to the readout line through a filter that passes the electromagnetic wave of the fourth frequency,
A measurement method for measuring the electromagnetic wave of the fourth frequency in the readout line. Applying a first electromagnetic wave including a component of a first frequency to a resonator having a Josephson junction;
Applying a second electromagnetic wave including the first frequency component and the second frequency component to the resonator;
Measuring electromagnetic waves propagated from the resonator through a filter;
A method for measuring the oscillation state of the resonator,
The resonator oscillates at a third frequency by the first electromagnetic wave, oscillates at the third frequency and a fourth resonance frequency by the second electromagnetic wave,
A measurement method in which a pass rate of the filter at the fourth frequency is higher than a pass rate of the filter at the third frequency. The pass rate of the filter at a fifth frequency included in one pass band of the filter is half of the peak value of the pass rate of the filter,
The pass rate of the filter at a sixth frequency included in the passband and higher than the fifth frequency is half of the peak value,
The fourth frequency is between the fifth frequency and the sixth frequency;
The measurement method according to claim 9, wherein the third frequency is lower than the fifth frequency or higher than the sixth frequency.

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